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curve #1799

y² + xy = x³ − 15403585x + 22080572297

a-invariants: [1, 0, 0, -15403585, 22080572297]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/6ℤ
conductor (N): 45225870
discriminant (Δ): 23261364854820864000000
Faltings height: 3.0458
naive height: 61.2639
primes of bad reduction: 2, 3, 5, 41, 83, 443
regulator: 16.393471939114918592412316942880975482387409
submitted by: hdeping
submitted at: 2026-09-25 15:04:15 UTC
last updated: 2026-09-25 15:04:15 UTC

Witness: 3 independent points log in to add more points →

(1634, 34883)
(17834, 2319083)
(2834, 33083)

Commentary

Specialization t=-5/2 of Eroshkin's exact rank-3 family with torsion Z/6Z (Dujella-Peral-Tadic, sec 5).

last edited by hdeping at 2026-09-27 08:31:49 UTC · history

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